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# PK/PD model library

Documentation under construction

The PK/PD model library is combining our library of standard pharmacokinetic models with a library of standard pharmacodynamic models.

The PK part is already described on the PK library page. Most PD models included in the PK/PD library can also be used alone (without a PK model) in the PD library, and some models from the PD library are only available alone. The complete list and full equations for PD models in the PD library is available in this document. Here we focus on the PD models of the PK/PD library because they are the most widely used.

PD models can be categorized by:

• the type of response linking the concentration of the drug in the central compartment $$C_C$$ to the effect E or to the response R. The effect can be either direct, or with an effect compartment, or an action on a turnover rate;
• the type of drug action on the response or on the rate. It can be a stimulation or an inhibition;
• the presence or absence of sigmoidicity in this drug action.

# Type of response

The response links the drug concentration $$C_C$$ to the effect $$E$$ or the response R via a function $$A^E$$ or $$A^R$$ modeling the action of the drug. The type of response specifies whether this action impacts directly the effect, or via an effect compartment or turnover rates. The content of the action function will be specified in the next section: type of drug action. To explore the differences in the types of response, we will see how they impact the PD output for a 1 compartment PK linear infusion model, with a stimulation action of the drug and without sigmoidicity.

## Direct

In case of a direct response, the effect $$E$$ directly relates to $$C_C$$ via

$$E = A^E(C_C)$$

Therefore the dynamics of the effect follow the dynamics of $$C_C$$ without any delay, meaning that as soon as $$C_C$$ starts decreasing, $$E$$ decreases as well, and the trajectory in the phase plane $$C_C$$ vs $$E$$ is a single line because it follows the same route during the increase and the decrease of the signals.

## Effect compartment

The site of action of the drug is often not be the same as the central compartment, and therefore a delay often appears between the PK and the PD measurements. To account for this delay it may be enough to add a single theoretical effect compartment with a drug concentration $$C_e$$ equal to the concentration at the site of action. A single transfer rate $$k_{e0}$$ is used between the central and the effect compartments and the effect now directly relates to $$C_e$$:

$$\frac{d C_e}{dt} = k_{e0}C_C – k_{e0}C_e$$

$$E = A^E(C_e)$$